Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

Abstract

A regime of very long meandering positive and negative streamwise velocity fluctuations, that we term ‘superstructures’, are found to exist in the log and lower wake regions of turbulent boundary layers. Measurements are made with a spanwise rake of 10 hot-wires in two separate facilities (spanning more than a decade of Reτ) and are compared with existing PIV and DNS results. In all cases, we note evidence of a large-scale stripiness in the streamwise velocity fluctuations. The length of these regions can commonly exceed 20δ. Similar length scales have been previously reported for pipes and DNS channel flows. It is suggested that the true length of these features is masked from single-point statistics (such as autocorrelations and spectra) by a spanwise meandering tendency. Support for this conjecture is offered through the study of a synthetic flow composed only of sinusoidally meandering elongated low- and high-speed regions. From detailed maps of one-dimensional spectra, it is found that the contribution to the streamwise turbulence intensities associated with the superstructures appears to be increasingly significant with Reynolds number, and scales with outer length variables (δ). Importantly, the superstructure maintains a presence or footprint in the near-wall region, seeming to modulate or influence the near-wall cycle. This input of low-wavenumber outer-scaled energy into the near-wall region is consistent with the rise in near-wall streamwise intensities, when scaled with inner variables, that has been noted to occur with increasing Reynolds number. In an attempt to investigate these structures at very high Reynolds numbers, we also report on recent large-scale sonic anemometer rake measurements, made in the neutrally stable atmospheric surface layer. Preliminary results indicate that the superstructure is present in the log region of this atmospheric flow at Reτ = 6.6×105, and has a size consistent with outer scaling.

Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

“…This behaviour of the peak is in agreement with the incompressible boundary layer results of Balakumar & Adrian (2007). Note that the actual length is believed to be underestimated by the hot-wire data due to meandering of these very large-scale structures (Hutchins & Marusic 2007;Ganapathisubramani et al 2007b). Furthermore, below λ x /δ = 1.3 the pre-multiplied power spectra are slightly affected by the response of the hot wire.…”

“…Furthermore, below y/δ = 0.7 the primary orientation of the structures in their correlation map falls within a narrow range of approximately 10 • with the streamwise direction, which is decreasing further as the wall is approached and is clearly different from the 45 • diagonal. It is, therefore, well possible, that the smaller 10 • angle reflects another phenomenon like the meandering of the low-speed zones causing a skewing with respect to the streamwise direction (Hutchins & Marusic 2007, and also visible in figure 2). Because of the variations in the relative orientations and distances between adjacent large-scale vortices in the individual snapshots, as also noted in Delo et al (2004), a statistic consistent with the instantaneous observations of a diagonal pattern is desirable.…”

“…Ganapathisubramani et al (2007b) even report lengths up to 40δ at y/δ = 0.2 in their supersonic boundary layer visualization based on high repetition rate PIV measurements and using Taylor's hypothesis. Long low-speed zones have also been found in incompressible turbulent boundary layers and pipe flow using a single hot-film (Kim & Adrian 1999) or a spanwise array of 10 hot wires to account for meandering of the low-speed zones (Hutchins & Marusic 2007). The width of the low-speed zones observed in the present experiments varies between 0.25δ and 0.4δ, which is consistent with earlier studies (Spina et al 1991;Tomkins & Adrian 2003;Ganapathisubramani et al 2006;Ringuette et al 2008), and the spanwise spacing between low-speed zones is typically between 0.5δ and 1.0δ.…”

Determining correlation and coherence lengths in turbulent boundary layer flight data

“…Under these conditions, the log region begins about 0.5 mm (100 wall units) from the wall. If the structures in the log region do impress a footprint on the wall pressure as suggested by Hutchins [18], the slightest modulation of the local pressure could result in a large variation in the impressions. Just such a mechanism is described by Bhat [5] as a possible explanation for the higher correlation decay rates he observed.…”

“…The center section exhibits behavior characteristic of the inner and outer layers. In a study by Hutchins [18], several different data sets are analysed to demonstrate the existence of very long structures in the log region and their influence on inner wall dynamics. Hutchins refers to a ''footprint'' impressed by structures in the log region on the inner wall.…”